Robust Reproducible Network Exploration

We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection, and call a collection of such edges a network. Our objective is thus rephrased as uncovering the network by selecting relevant edges, referred to as the network exploration. Our methodology is based on multiple testing for the presence or absence of each edge, designed to ensure statistical reproducibility via controlling the false discovery rate (FDR). In particular, we carefully construct $p$-variables, and apply the Benjamini-Hochberg (BH) procedure. We show that the BH with our $p$-variables controls the FDR under arbitrary dependence structure with any sample size and dimension, and has asymptotic power one under mild conditions. The validity is also confirmed by simulations and a real data example.